A flat car of mass m0 starts moving to the right due to a constant horizontal force ‘F’ at t = 0. Sand spills on the flat car from stationary hopper, the velocity of loading is constant and is equal to u kg s−1. Then( A )initial acceleration is equal to F/ m0( B )acceleration at time t is F/ m0+ ut( C )initial acceleration is less than F/ mo( D )initial acceleration is greater than F/ m0

Here you should specify clearly within the force begin to act at time equal to zero or send Falls at time equal to zero if send Falls at timing 0 then initial acceleration is force divided by M and any time t the mass of the car and become m plus UT then again acceleration equal to force divided by mass

Always apply the momentum equation, taking into account both the momentum of the loaded car (the varying-mass object) and also the momentum of the added mass. In principle, F=ma is valid only for constant mass. It comes out from the momentum equation that you get F=m(t)a when the variable mass object and the added or removed mass have the same velocity. That was valid for the leaking-out sand, but it is not true for this problem. The falling-in sand has zero horizontal velocity, while the car has velocity v. The added mass has to be accelerated to the velocity of the car, it is done by the interaction with the car and the sand in it. The added sand is accelerated by that interaction force, and the opposite force acts on the car. So it is not accelerated by F alone, but by F-μv.